Chapter 4

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Chapter 4

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4.1

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8 What you’ll learn about

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Absolute (Global) Extreme Values

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Local (Relative) Extreme Values

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Finding Extreme Values

…and why

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9 Absolute Extreme Values

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10 The Extreme Value Theorem

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12 Local Extreme Values

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13 Local Extreme Values

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14 Critical Points

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15 Example

Finding Absolute Extrema

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16 Example

Finding Extreme Values

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4.2

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18 Quick Review

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20 What you’ll learn about

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Mean Value Theorem

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Physical Interpretation

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Increasing and Decreasing Functions

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Other Consequences

…and why

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21 Mean Value Theorem for Derivatives

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22 Example

Explore the Mean Value

Theorem

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23 Increasing Function, Decreasing Function

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24 Corollary: Increasing and Decreasing

Functions

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27 Corollary: Functions with the Same

Derivative Differ by a Constant

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4.3

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31 Quick Review

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35 What you’ll learn about

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First Derivative Test for Local Extrema

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Concavity

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Points of Inflection

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Second Derivative Test for Local Extrema

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Learning about Functions from Derivatives

…and why

Differential calculus is a powerful problem-solving tool

precisely because of its usefulness for analyzing

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4.4

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57 What you’ll learn about

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Examples from Mathematics

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Examples from Business and Industry

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Examples from Economics

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Modeling Discrete Phenomena with Differentiable

Functions

…and why

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62 Minimizing Average Cost

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4.5

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66 What you’ll learn about

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Linear Approximation

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Newton’s Method

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Differentials

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Estimating Change with Differentials

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Absolute, Relative, and Percent Change

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Sensitivity to Change

…and why

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68 Example

Finding a Linearization

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69 Procedure for Newton’s Method

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4.6

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79 Quick Review Solutions

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80 What you’ll learn about

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Related Rate Equations

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Solution Strategy

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Simulating Related Motion

…and why

81 Strategy for Solving Related Rate Problems

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82 Strategy for Solving Related Rate Problem

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89 Quick Quiz

for Sections 4.4-4.6

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90 Quick Quiz

for Sections 4.4-4.6

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98 Chapter Test Solutions

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99 Chapter Test Solutions

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